The sum of the measures of the three angles of any triangle is 180°. In the illustration, the measure of 2 (angle 2) is 7° larger than the measure of 1. The measure of 3 is 31° larger than the measure of 2. Find each angle measure.
angle 1 = x
angle 2 = x + 7
angle 3 = x + 7 + 31
x + x + 7 + x + 7 + 31 = 180
Solve for x, measure of angle 1.
Then,
angle 2 = x + 7
angle 3 = x + 7 + 31
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what is the meaure of abc anglea
To solve this problem, we need to use the information given and the fact that the sum of the angles of a triangle is 180°.
Let's start by assigning variables to the angles. Let's call the measure of angle 1 'x'. According to the problem, angle 2 is 7° larger than angle 1, so angle 2 is 'x + 7'. Angle 3 is 31° larger than angle 2, so angle 3 is '(x + 7) + 31'.
Now, we can write an equation based on the sum of the angles of a triangle:
Angle 1 + Angle 2 + Angle 3 = 180°
Substituting the values we assigned for each angle:
x + (x + 7) + [(x + 7) + 31] = 180°
Now, we can simplify the equation:
3x + 45 = 180°
Next, let's isolate the variable:
3x = 180° - 45
3x = 135°
Finally, divide both sides of the equation by 3 to solve for x:
x = 135° / 3
x = 45°
Now that we have the value of x, we can find the measure of each angle:
Angle 1 = x = 45°
Angle 2 = x + 7 = 45° + 7° = 52°
Angle 3 = (x + 7) + 31 = 52° + 31° = 83°
Therefore, Angle 1 measures 45°, Angle 2 measures 52°, and Angle 3 measures 83°.